The Annals of Probability

The Support of Measure-Valued Branching Processes in a Random Environment

D. Dawson, Y. Li, and C. Mueller

Full-text: Open access

Abstract

We consider the one-dimensional catalytic branching process introduced by Dawson and Fleischmann, which is a modification of the super-Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On the other hand, the super-Brownian motion has compact global support. We find that all nonnegative stable random measures lead to compact global support, and we give an example of a very rarified Levy process which leads to noncompact global support.

Article information

Source
Ann. Probab., Volume 23, Number 4 (1995), 1692-1718.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176987799

Digital Object Identifier
doi:10.1214/aop/1176987799

Mathematical Reviews number (MathSciNet)
MR1379164

Zentralblatt MATH identifier
0853.60065

JSTOR
links.jstor.org

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Keywords
Stochastic partial differential equations branching processes Levy processes support

Citation

Dawson, D.; Li, Y.; Mueller, C. The Support of Measure-Valued Branching Processes in a Random Environment. Ann. Probab. 23 (1995), no. 4, 1692--1718. doi:10.1214/aop/1176987799. https://projecteuclid.org/euclid.aop/1176987799


Export citation